Unit 6: Quadratic Functions Algebra II with Trigonometry
Unit 6:
Quadratic Functions
LESSON #3:
THE PARABOLA
APPLICATIONS AND
WORD PROBLEMS
Applications of Parabolas
Lesson #3 Applications and Word Problems with Parabolas
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Unit 6: Quadratic Functions Algebra II with Trigonometry
Ex 1) A toy rocket is launched from an 89m tall platform. The equation for the object’s height, , at a time seconds after launch is .
.
(a) How long does it take for the toy rocket to reach its maximum height?
(b) What is the maximum height of the toy rocket?
(c) At what time does the toy rocket return to the ground, rounding to the nearest second?
(d) When will the projectile reach 50m above the ground?
Ex 2) Alex is standing on a hill 80 feet high. He throws a baseball upward with an initial velocity of 64 feet per second. The height of the ball, , in terms of the time seconds since the ball was thrown is .
(a) How long does it take for the ball to reach its maximum height?
(b) What is the maximum height of the ball?
(c) What is the height of the ball after 2 seconds?
(d) At what time does the ball hit the ground?
Lesson #3 Applications and Word Problems with Parabolas
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Unit 6: Quadratic Functions Algebra II with Trigonometry
Ex 3) The weekly profit function in dollars of a small business that produces fruit jams is .
, where is the number of jars of jam produced and sold. (a) Find the number of jars of jam that should be produced to maximize the weekly profit. (b) Find the maximum profit. Ex 4) Amelia throws a set of keys up to her brother, who is standing on a third‐story balcony with his hands 38 feet above the gorund. If Amelia throws the keys with an initial velocity of 40 feet per second, the equation , gives the height of the keys after seconds. (a) How long does it take the keys to reach their highest point?
(b) How high do the keys reach?
(c) Will Amelia’s brother be able to catch the keys? Explain. Lesson #3 Applications and Word Problems with Parabolas
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Unit 6: Quadratic Functions Algebra II with Trigonometry
Ex 5) Tom throws a football with an initial velocity of 80 feet per second from a height of 6 feet above the ground. equation, .
gives the path of the ball, where is the height and is the horizontal distance the ball travels. (a) What is the maximum height reached by the football?
(b) A receiver catches the ball 3 feet above the ground. How far as the ball traveled horizontally when the receiver catches it?
Ex 6) An engineer is designing a flashlight using a parabolic reflecting mirror and a light source. The casting has a diameter of 6 inches and a depth of 4 inches. What is the equation of the parabola used to shape the mirror? At what point should the light source be placed relative to the mirror’s vertex?
4
in
6
in
Lesson #3 Applications and Word Problems with Parabolas
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